A generalization of Allen's interval-based approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semi-intervals rather than intervals are used as the basic units of knowledge. Semi-intervals correspond to temporal beginnings or endings of events. We demonstrate the advantages of reasoning on the basis of semi-intervals: 1) semi-intervals are rather natural entities both from a cognitive and from a computational point of view; 2) coarse knowledge can be processed directly; computational effort is saved; 3) incomplete knowledge about events can be fully exploited; 4) incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps; 5) there is no trade-off in computational strength for the added flexibility and efficiency; 6) for a natural subset of Allen's algebra, global consistency can be guaranteed in polynomial time; 7) knowledge about relations between events can be represented much more compactly.

We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORD-Horn subclass is a polynomial-time problem and show that the path-consistency method is sufficient for deciding satisfiability. Further, using an extensive machine-generated case analysis, we show that the ORD-Horn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. This work has been supported by the German Ministry for Research and Technology (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project. 1 1 Introduction Temporal information is often conveyed qualitatively by specifying the relative positions of time intervals such as ". . . point to the figure while explaining the performance of the system . . . "...

The notion of time is ubiquitous in any activity that requires intelligence. In particular, several important notions like change, causality, action are described in terms of time. Therefore, the representation of time and reasoning about time is of crucial importance for many Artificial Intelligence systems. Specifically during the last 10 years, it has been attracting the attention of many AI researchers. In this survey, the results of this work are analysed. Firstly, Temporal Reasoning is defined. Then, the most important representational issues which determine a Temporal Reasoning approach are introduced: the logical form on which the approach is based, the ontology (the units taken as primitives, the temporal relations, the algorithms that have been developed,. . . ) and the concepts related with reasoning about action (the representation of change, causality, action,. . . ). For each issue the different choices in the literature are discussed. 1 Introduction The notion of time i...

. Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints represent the possible temporal relations between them. The main tasks are two: (i) deciding consistency, and (ii) answering queries about scenarios that satisfy all constraints. This paper overviews results on several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifying tractable subclasses, (ii) developing exact search algorithms, and (iii) developing polynomial-time approximation algorithms. Most available techniques are based on two principles: (i) enforcing local consistency (e.g. path-consistency), and (ii) enhancing naive backtracking search. Keywords: Temporal Constra...

A planning tool box is a set of software modules implementing different planning algorithms, techniques, and representation languages. A planning system designer can use these modules---and possibly additional own ones--- for building a whole family of generic or application planners. The paper explains the concept and outlines work on developing such a tool box. In particular, it identifies descriptions of planning domain characteristics as a topic in planning theory from which results are needed for building a tool box, yet are missing. Overture: The tool box idea, and the paper Writing effective programs for difficult problem classes, like planning, would normally require to narrow down the range of the program's applicability: The more generality is admitted, the more overhead results. In consequence, it makes sense to tailor a planning system such that it fits closely the intended application domain or class of applications. In research, concentration on a single planning paradi...

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Generalized intervals are finite ordered sequences of time points (Allen's calculus is the special case of ordered pairs). In this paper, we show why generalized intervals are good candidates for reasoning about complex events (with more than two crucial time points): Binary relations between them can be easily encoded; the conversion and composition operations on disjunctive relations provide them with a structure of a relation algebra; although the whole calculus is not tractable in general, there exists a subclass of disjunctive relations, which is easily characterized in geometric terms, which is tractable (in Allen's cases, this subclass coincides with the ORD-Horn class); for binary temporal networks on this subclass, consistency is decidable in cubic time by testing path-consistency; moreover, a scenario can be computed in cubic time without backtrack (in quadratic time for consistent networks). Finally, the strong theory of n-intervals (generalized intervals with n time points)...

In this paper we describe a core ontology for N-dimensional spatial reasoning. The ontology is intended to support both quantitative and qualitative approaches and is expressed using set notation. Using the ontology; spatial domains of discourse, spatial objects and their attributes, and the relationships that can link spatial objects can be expressed in terms of sets, and sets of sets. The core ontology has been emphparameterised to express a number of task dependent ontologies in application areas such as Geographic Information Systems (GIS), noise pollution monitoring, environmental impact assessment, shape fitting, timetabling and scheduling, and AI problems such as the N-queens problem. We illustrate this parameterisation by using the core ontology to express both Allen's interval calculus, and Egenhofer's "9-Intersection" approach to topological spatial reasoning. Although there is still much work to do, the directed task ontologies that have been investigated indicate that the c...

This paper shows the close relationships between qualitative representations and default reasoning. These relationships are manifold: On the one hand, qualitative representations and defaults can be considered as alternate ways to cope with fuzzy or incomplete knowledge. On the other hand, defaults and their associated revision mechanisms are also needed in the qualitative approach to handle the fact that they are inherently under-determined. Furthermore, in the case of spatial representations the structural similarity between the representing and the represented worlds prevents us from violating constraints corresponding to basic properties of the represented world, which would otherwise have to be restored through revision mechanisms at great cost.

A generally applicable approach to N-dimensional spatial reasoning is described. The approach is founded on a unique representation based on ideas concerning "tesseral" addressing. This offers many computational advantages including minimal data storage, computationally efficient translation of data, and simple data comparison, regardless of the number of dimensions under consideration. The representation allows spatial attributes associated with objects to be expressed simply and concisely in terms of sets of addresses which can then be related using standard set operations expressed as constraints. The approach has been incorporated into a spatial reasoning system --- the SPARTA (SPAtial Reasoning using Tesseral Addressing) system --- which has been successfully used in conjunction with a significant number of spatial application domains. Keywords: Spatio-Temporal Reasoning, Tesseral Addressing, N-Dimensional information processing. 1 INTRODUCTION A versatile and generally applicabl...